A Classification-Based Surrogate-Assisted Evolutionary Algorithm for Expensive Many-Objective Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have been developed mainly for solving expensive optimization problems where only a small number of real fitness evaluations are allowed. Most existing SAEAs are designed for solving low-dimensional single or multiobjective optimization problems, which are not well suited for many-objective optimization. This paper proposes a surrogate-assisted many-objective evolutionary algorithm that uses an artificial neural network to predict the dominance relationship between candidate solutions and reference solutions instead of approximating the objective values separately. The uncertainty information in prediction is taken into account together with the dominance relationship to select promising solutions to be evaluated using the real objective functions. Our simulation results demonstrate that the proposed algorithm outperforms the state-of-the-art evolutionary algorithms on a set of many-objective optimization test problems.

I. Introduction

Multiobjective optimization problems (MOPs) are commonly seen in the real world, e.g., electrical engineering [1], industrial scheduling [2], and robotics [3]. These problems aim to simultaneously optimize more than two often conflicting objectives, which can be mathematically formulated as follows: \begin{align} \text {minimize}~~&F(x)=\left ({f_{1}(x),f_{2}(x),\ldots,f_{m}(x)}\right)\notag \\ \text {subject to}~~&x\in X \end{align} where is the number of objectives and is the decision vector [4]. A large number of multiobjective evolutionary algorithms (MOEAs) were proposed in the past decades, e.g., the region-based selection algorithm (PESA-II) [5], the improved strength Pareto evolutionary algorithm [6], the elitist nondominated sorting genetic algorithm (NSGA-II) [7], the improved indicator-based evolutionary algorithm [8], and the MOEA based on decomposition (MOEA/D) [9]. These algorithms have been shown to be effective in solving MOPs with two or three objectives [10].